Bivariate_Normal_Analysis

This project demonstrates bivariate normal distribution analysis including scatter plots, confidence ellipses, histograms, contour plots, normality tests, and Pearson correlation confidence intervals.

The goal is to generate a synthetic bivariate normal dataset and analyze its properties. Key features include:

1. Data Generation

   • Created a 2D dataset with specified mean vector and covariance matrix.

2. Visualization

   • Scatter plots with 50% and 90% confidence ellipses.
   • Histograms with overlaid 1D normal PDFs.
   • Contour plots showing joint PDF of X and Y.

3. Normality Testing

   • Chi-square test in 2D bins.
   • KS and Shapiro-Wilk tests (manual implementation possible).

4. Correlation Analysis

   • Computed Pearson correlation coefficient.
   • Constructed 95% confidence interval for correlation using Fisher's z-transform.

---

Technologies Used

• Python 3
• NumPy (data generation and calculations)
• Matplotlib (visualization)
• SciPy (statistical tests)
• Seaborn (scatter plots)